Saturday, July 28, 2012

Is There a Hot Hand in Olympic Archery?

Many Olympic sports got underway today in London and environs. One event that I watched today and that potentially is an excellent candidate for hot-hand analysis is archery. As I discuss in my book and in this video, sports that are most conducive to streakiness are those that consist of relatively simple motions that can be repeated with little delay between attempts.

The event I watched today, specifically, was the men's team archery final, between Italy and the United States. Each team has three shooters or archers. When it's a team's turn, each member will get one shot, so that several minutes will elapse between consecutive shots by any one person. This aspect is not optimal for detecting streakiness. Also, each member gets only eight attempts. Thus, even when aggregating over all six participants, the total number of shots is too small for traditional statistical analysis.

Still, for curiosity's sake, I thought I'd examine the arrow-shooting sequences. Archers receive 10 points for their team by hitting the bullseye, and 9, 8, 7, etc., for landing their arrow in each respective outward ring from the center. As I depict in the following chart, no archer earned below an 8 on any shots. Archery matches (in the team format, at least) are organized into four sets (known as "ends") of six shots each. Because each archer on a three-person team shoots twice in one end, I designate the shots as "1a" for first shot of the first end, "1b" for second shot of the first end, and so forth.

I decided to simplify my little analysis by dividing
outcomes into two categories: 10's (bullseyes) and non-10's (i.e., 8 or 9). The "hot hand" concept, in the sense of "success begetting success," suggests that when an archer shoots a bullseye (10-pointer), he or she should have a higher probability than usual of hitting a bullseye on his or her next shot, as well.

Highlighted in gold in the above chart are all attempts that immediately followed a 10. For example, USA Shooter A earned a 10 on his 3a shot, so his next cell (for 3b) is highlighted in gold. Shot 3b was also a 10, so 4a is gold. Unshaded white cells represent attempts immediately following a non-10. Each shooter's first attempt (green cells) is excluded from the analysis, because he had no prior attempts at that point.

As described above, the hot hand hypothesis predicts that 10's will be more common (percentagewise) in the gold cells than in the white cells. As shown at the bottom of the chart, this pattern is exactly what was found: Bullseyes occurred on 46% of the arrows fired after the same archer had hit a bullseye on his previous shot. In contrast, bullseyes occurred on only 28% of the arrows fired after the same archer had scored an 8 or 9 on his previous shot.

Given the small sample, the difference between 46% and 28% was not statistically significant, but it was in the direction predicted by hot-hand reasoning. Considering that the archers faced delays of several minutes between their own shots, this result isn't bad!

I will keep my eye out for additional archery events during these games (men's individual, women's team and individual) and I invite readers to do the same. Statistics for all sports are available at NBCOlympics.com. For the men's team archery final, all the shot-by-shot data were available online (albeit organized in a different format than I used), so I was able to verify the scores I wrote down while watching the event against what was listed on the website. However, as a precaution, I would urge readers interested in conducting their own analyses to write down as much data as they can while watching events on television.